Number properties - please help

Question

Q. Two different 3 digit numbers contain the digits 1,2,3,5,6,9. Each digit of the two numbers is different from the others. What is the least possible difference between these two numbers?

A. 19
B. 12
C. 8
D. 33
E. 29

This obviously involves plugging in numbers and can take a long time. Can anyone please explain the shortest route to this Q? Also what are the chances that such Q's appear on the actusl exam?

Thanks
NAD

nov79 · Answer

Try to put in front the largest numbers- 5,6 (they are the closest ones)
so we have the hundredth digit.
Now the tenth digit - lets put 1, 9 (the next closest ones.
So we have 59, 61. We have only 2 numbers left- 3,2.

Thus, the two numbers are: 593, 612 - and the difference between them is 19!

This problem can be solved with only logic.

Sarang · Answer

Take one number ending nearer to the 90s and the other that ends nearer to the 10s.

For 1st:- To take nearer to 90s, put 9 in 10s digit- For ex- 296

Take the other number nearer to 10s (like 515, 611 etc) - put lesser number in the 100s place
The next available lesser number that brings closer to 300 is - 3; So put 3 at 100s place the other 2 available numbers are - 1 & 5---> 315

315-216=19

Answer:- A

Sarang · Answer

Sorry guys, but couden't find formuletic answer........

VeritasPrepBrian · Answer

Hey Sarang,

No need to apologize - that was perfect! That was as systematic an answer as I think you can come up with. When they ask you to minimize the difference, you should start thinking about priorities. The biggest difference in a subtraction problem of 3-digit numbers is in the hundreds digits...9XY - 1AB is going to be a huge gap regardless of X, Y, A, and B, so we need to keep the hundreds close together. So Priority One is:

Hundreds Digits Adjacent

Next, the biggest possible spread is in the Tens digits, so we want those together. But here we need to think of how to keep them together. 340 - 230 is still a big gap of over 100. If we could have 301-299, we'd be as close together as possible, so we ideally want to use the 0 or 1 as the Tens digit of the bigger number and 9 as the Tens digit of the smaller number to keep them close - we want to maximize the smaller number and minimize the larger number. We have 1 and 9 available, so we want 9 for the smaller and 1 for the larger. Priority Two becomes:

Tens Digits: 9 and 1

Then we want to narrow the gap for what's left, and we'll still have adjacent digits left to use so we want to maximize the smaller number and minimize the large number to keep them close.

Since we have the 1 and 9 earmarked for the Tens digits and we need adjacent numbers for the Hundreds, we could use:

61_
59_

or

31_
29_

Either way, the remaining digits are adjacent, so we could pick either:

612
-593
= 19

or

315
-296
= 19

Either way, the correct answer is 19.

nonameee · Answer

How realistic is this question on the real GMAT? I've followed the same logic as Brian, but I came up with the numbers 235-196 and couldn't quickly find closer numbers. Thank you.

Number properties - please help

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